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1 Answer
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It's not clear what is the point in doing that, but if you're an admin you can do chmod o+r pg_hba.conf to let a non-admin read it.

There are two ways in pgAdmin3 to access those files:

by reading the file system (if it runs on the same host than the server). This corresponds to the File->Open *.conf commands. With that method, permission-wise, pgAdmin is not special, it's like a text editor or a pager.

through the DB connection, with Tools->Server configuration. This requires the adminpack contrib module installed server-side. In the case of Ubuntu, I'm not sure it would work because the configuration files are not inside the data directory below /var, they're under /etc/... and the server-side functions involved are not supposed to reach anything outside the data directory. But if/when this method does work, it's the postgres process that reads the files, so the permissions shown in the question are good enough.

I was able to access the pg_hba.conf with pgAdmin reading the file system only after I gave other the read permission. Still not sure (& curious) why they were different in the first place. I am afraid Tools → Server Configuration → pg_hba.conf does not work with this set up. Which I find odd as I can work with postgresql.conf without any problems using both of the ways that you have outlined above.
– dw8547May 11 '17 at 8:05

as per your second point & this post postgresql.org/message-id/…, it should not be possible to edit either pg_hba.conf or postgresql.conf so I'm finding this even odder. (The extension adminpack is installed in all the DBs.)
– dw8547May 11 '17 at 8:21